What are the different oxidation states exhibited by the following elements: (a) Titanium (b) Nickel (c) Vanadium Also comment on the colour and magnetic properties of the compounds in these oxidation states.

In transition metal compounds, d-orbital transitions are responsible for their vivid colors. These transitions involve the movement of an electron between different levels of d orbitals within the same atom. As these orbitals differ slightly in their energy levels, when light interacts with the compound, certain wavelengths are absorbed to promote electrons from a lower to a higher d-orbital. The remaining wavelengths of light that are not absorbed are reflected or transmitted, and these give rise to the observed color.

For instance, in titanium compounds, a fully filled or half-filled d-orbital setup means that d-d transitions cannot occur, leading to colorless compounds. On the other hand, nickel in a +2 oxidation state shows colors due to two unpaired electrons allowing such transitions. Similarly, vanadium compounds exhibit a variety of colors because of multiple oxidations states, each with different electron configurations in its d-orbitals, enabling diverse d-d transitions.

The variety of colors exhibited by transition metal compounds is largely due to the d-orbital transitions discussed earlier. The specific colors seen can be an indicator of the oxidation state of the metal within the compound.

For clarity, let's consider nickel (+2 oxidation state), which often results in green or blue compounds. This is a consequence of certain wavelengths being absorbed for the d-d orbital transitions related to that particular oxidation state, corresponding to the energies needed to pair up or unpair the electrons. Vanadium compounds are particularly illustrative - vanadium(II) compounds are often violet, vanadium(III) usually green, and vanadium in higher oxidation states can show colors from blue to yellow due to different types of electron transitions occurring within the d orbitals.

The magnetic properties of transition metal compounds are intricately linked to the presence of unpaired electrons within their d orbitals. Diamagnetic compounds are those that have all their electrons paired and tend to be weakly repelled by a magnetic field. Paramagnetic compounds possess unpaired electrons and are attracted to magnetic fields to varying degrees.

For instance, titanium compounds, which are generally diamagnetic, feature no unpaired electrons and thus have a weak interaction with magnetic fields. On the other hand, nickel compounds in the +2 oxidation state are paramagnetic due to the presence of two unpaired electrons, which makes them responsive to magnetic fields. The vanadium compounds, depending on their particular oxidation state and electron configuration, can showcase a range of magnetic behaviors from diamagnetism to various forms of paramagnetism.